The strops are a great idea! They would also address one of the worst features of in-foil headsails which is the lack of attachment (other than the corners) during a hoist or douse. Shorthanded take-downs can get quite exciting in a serious breeze, and I once nearly broke a finger trying to prevent a sail being swept over the side when a part of it fell into the sea.
Absolutely agree that using a
furler as a reef is a non-starter.